Purely anecdote, but zero companies I know in Germany, Italy or France are doing this. (The ones in Switzerland are.)
There is a cosmetic fix that produces an email so there is something to show a regulator if they come knocking. The logic being investing anything more than that is a crap shoot, given nobody knows how each of the EU’s 28 data regulators will interpret the rules.
But from what I have seen, most of that time was spent on the legal and policy site, not on actually implementing the technical changes required to properly handle, store and delete data.
I can absolutely guarantee you that the overwhelming majority EU companies could not properly carry out a GDPR deletion request.
In France in particular the right to access/change/delete any and all data a company has on you was there long before GDPR (by decades) so most serious company are well used and prepped for it.
They range from start-ups to national champions, but I won't disagree with you on the poor organization of most European companies point. Everyone one re-papered existing systems to some degree of compliance. Given nobody agrees on what full compliance is, they're all right in their own ways.
With Blizzard it went a bit different. They do have online automated tool to download your own data, but with a twist: they refused to provide what they consider security risk information. They did provide a lot of data (even years old chat logs) but did not provide the information I was looking for: list of processes running on my PC, which they scan periodically, as an anti-cheating mechanism. I went further and filed a GDPR infringement complaint to the national office but it failed. Last option was to sue, but I gave up.
Both Epic and Blizzard are US based.